Theorems · Theorem · algebraic geometry

RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S} {n : ℕ},
  RingHom.IsStandardSmoothOfRelativeDimension n f → ∃ g, g.comp MvPolynomial.C = f ∧ g.Etale

Every standard smooth homomorphism R → S factors into R -> R[X₁,...,Xₙ] → S where n is the relative dimension and R[X₁,...,Xₙ] → S is etale.

Defined in

Mathlib.RingTheory.RingHom.StandardSmooth

Cited by

1 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRing